Two days after incumbent Sen. David Vitter suffered a stunning loss in the race for governor and said he’ll call it quits on his political career, two congressional Republicans announced their bids for Louisiana’s Senate seat.

Mr. Boustany, who’s been eyeing the seat for several months, was the first major name to pull the trigger on announcing a run for what’s likely to be one of the GOP’s most sought-after seats.

“Our state needs leadership. We need a Senator who can lead in times of challenge, offer solutions to problems, and bring unity,” Mr. Boustany, a six-term Republican, tweeted Monday. He added that he was planning a formal announcement to launch his campaign in his hometown of Lafayette.

Mr. Fleming also announced Monday that he would be running for Mr. Vitter’s seat and that an official campaign launch would happen “in the near future.”

“Louisiana wants a leader that will take their values to D.C. and will fight for them without wavering,” Mr. Fleming said in a statement.

Republicans are confident they can hold the seat, and boast of a wealth of other candidates too, including state Treasurer John Kennedy, Public Service Commissioner Scott Angelle, and retired Air Force officer Rob Maness, who ran third in the 2014 Senate race.

On the left, though, viable options are scarce. One name that has been floated is New Orleans Mayor Mitch Landrieu, who turned down the chance to run for governor this year, and may choose not to run for the Senate, where his sister, Mary L. Landrieu, lost her seat in the 2014 election.

Mr. Vitter’s seat has been regarded as a potentially open seat for months, as he would have had to give it up anyway had he won the governorship.

“I had decided when I decided to make this race with [wife] Wendy that I wanted to pursue new challenges outside the Senate no matter what,” Mr. Vitter said in his concession speech after losing a run-off election to Democrat John Bel Edwards, who crushed him 56 percent to 44 percent. “I reached my personal term limit.”

Mr. Vitter’s decision helps Republicans in Washington avoid a conundrum. If he’d tried to run for his Senate seat again, it would have forced the National Republican Senatorial Committee to spend money helping him keep it — money that the NRSC would prefer to be spending to hold other seats, such as Florida, rather than in deep red Louisiana.

“Senator Vitter would’ve been seen as a target for Democrats to go after, or other Republicans. But by taking himself out of the competition, he changed that question,” said Pearson Cross, associate professor of political science at University of Louisiana at Lafayette.

That Mr. Vitter lost at all in Louisiana, which has been tilting further toward the GOP in recent years, is the outcome of unique circumstances.

Current Gov. Bobby Jindal, who just ended his presidential campaign last week, “mucked up the state finances so badly,” Mr. Cross said. That left the Republicans seeking to succeed him attacking each other with vicious ads. One of Mr. Vitter’s GOP opponents even endorsed Mr. Edwards, the Democrat, in the run-off.

Mr. Vitter, meanwhile, still suffered from a prostitution scandal.

Next year’s Senate race, meanwhile, won’t have baggage from either Mr. Vitter or Mr. Jindal overhanging it, said Edward Chervenak, a political scientist at University of New Orleans and director of their UNO Survey Research Center.

“Jindal was poison for David Vitter,” Mr. Chervenak said. “People were unhappy with the direction of the state, extremely disapproving of the current governor and I think some of that cost David Vitter votes.”

Louisiana has a complex election system, with no partisan primaries and everybody put into the same pot. If no candidate wins a majority of the vote in the first go-around, also known as a “jungle primary,” the top two vote-getters are pitted in a run-off. This could conceivably lead to an election between two candidates from the same party.

It is possible, but unlikely, that Mr. Jindal would run for Senate now that his presidential campaign is over and he will no longer be governor, said James Garand, a political scientist at Louisiana State University.

Mr. Boustany serves on the House Ways and Means Committee, where he has been one of the major opponents of Obamacare. He has stepped up his fundraising and has about $1.4 million cash on hand for his congressional account, which can be transferred to a senatorial account.

Mr. Fleming is a more conservative congressman and a member of the the House Freedom Caucus, a group that played a role in ousting former Speaker John A. Boehner. He has about $2.3 million cash on hand, and can afford to partially self-fund his campaign.

Mr. Kennedy — a former Democrat who switched parties in 2007 — just won his fifth term as the state treasurer in October. He has run for Senate twice before, once as a Democrat and once as a Republican. He has $2.5 million on hand, and is a popular statewide figure.

Mr. Maness is a tea party favorite who ran unsuccessfully for the Senate in 2014. He is running again and said he was campaigning as an outsider.

Democrats will have to try to find a candidate, but have a slim chance of capturing the seat, Mr. Garand said.

“It’s a national election, so there’s a different electorate with a higher share of individuals with a lower level of income who come out in presidential elections who don’t come out in midterms,” he said. “There’s a higher share of African-Americans and racial minority groups.”